The US Department of Justice has filed criminal charges against 28 green card holders in California accused of fraudulently registering to vote and casting illegal ballots. ... A justice department spokesperson said 21 of the 28 defendants had cast unlawful ballots.
If they did, I have no sympathy for them. US Citizenship and Immigration Services expressly informs green card applicants that "[p]ermanent residents cannot vote in federal, state, or local elections." Do the crime, do the time.
As for registration, given that so many states have "motor voter" laws that may automatically register people who get drivers' licenses, etc., I'd say the criterion for prosecution should be "did this person actually vote or attempt to vote?" It's entirely possible that a green card holder gets a driver's license, gets automatically registered due to government error, and never even notices, let alone tries to use the registration to actually vote.
A lot of the news coverage of such things, including the story linked above, asserts that "[v]oting by noncitizens is extremely rare," and that seems to be the case.
In fact, this set of arrests tends to confirm that. California claims 22 million registered voters. The US Department of Justice has been able to find a whopping 21 alleged non-citizen voters. That's less than 1 in a million registered voters. Have any statewide elections in California ever been decided by one one-millionth of votes cast? Or even by, say, 21 votes?
